A065813 Least m such that (p^(2*m+1)-1)/(p-1) is a prime, where p = prime(n).

1, 1, 1, 2, 8, 2, 1, 9, 2, 2, 3, 6, 1, 2, 63, 5, 1, 3, 9, 1, 2, 2, 2, 1, 8, 1, 9, 8, 8, 11, 2, 1, 5, 81, 3, 6, 8, 3, 1, 1, 9, 8, 8, 2, 15, 288, 20, 119, 2, 5, 56, 2, 8, 3, 11, 2

Offset: 1

Author

Vladeta Jovovic and Labos Elemer, Nov 13 2001

Keywords

• hard
• nonn

Examples

			a(5) = 8 because ithprime(5) = 11, (11^(2*m+1)-1)/10 is not a prime for m = 1..7 and (11^17-1)/10 = 50544702849929377 is a prime.
		

Links

• Andy Steward, Prime Generalized Repunits

Crossrefs

Cf. A000005, A000203, A000040, A065403-A065405, A000043, A001348, A065854.

Programs

Mathematica

Do[p=Prime[w]; s=DivisorSigma[1, (p^r)^2]; z=DivisorSigma[0, (p^r)^2]; If[PrimeQ[s], Print[{p, r, p^r, s, z}]], {w, 1, 100}, {r, 1, 100}] For w=12, this prints out first {37, 6, 2565726409, 6765811783780036261, 13}.
lm[n_]:=Module[{m=1},While[!PrimeQ[(n^(2m+1)-1)/(n-1)],m++];m]; lm/@Prime[ Range[ 56]] (* Harvey P. Dale, Feb 16 2014 *)

PARI

{ allocatemem(932245000); for (n=1, 100, x=prime(n); s=x^2; q=x - 1; m=1; while (!isprime(((x*=s) - 1)/q), m++); write("b065813.txt", n, " ", m) ) } \\ Harry J. Smith, Oct 31 2009